Finite Group Databasebeta

← #14654514

Subgroups — #14654514

Order 2816.

602 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078076C211yesmaximal, characteristic
2#13073974C211yesmaximal, characteristic, complemented
3#13067176C211yesmaximal, characteristic, complemented
4#13067045C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#3103C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#67002—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#481—21no—
13C11×#475—21no—
14C11×#460—21no—
15C11×#448—21no—
16C4×C11×SD16—22no—
17C11×#431C2211yescharacteristic
18#10622845—21no—
19#10622844—21no—
20#10622696—21no—
21#10622685—21no—
22#10622670—22no—
23#10622605—21no—
24#10622602—22no—
25#10622552—21no—
26#10622549C2211yescharacteristic
27#10622541—21no—
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30#10622175—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622097—22no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C2×C11×SD16—22no—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53#67002—42no—
54#67002—42no—
55C2×#4325—22no—
56C2×#4323—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×#4318—21no—
64C4×D44—21no—
65C4×D44—21no—
66C4×D44—21no—
67C4×D44—21no—
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×#103—22no—
71C11×#102—22no—
72C11×C22⋊C8—21no—
73C4×C8×C11D412yes—
74#66899—22no—
75#66896—22no—
76C11⋊#95—22no—
77C11⋊#95—21no—
78C11⋊#95D412yes—
79C22⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yes—
83C4×C11⋊C8—21no—
84#9998—111nomaximal, Sylow
85C23×D11—21no—
86C11×#41—41no—
87C11×#41—41no—
88C11×#41—41no—
89C11×#41—41no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—42no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44SD1612yescomplemented
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11—82no—
115C11×SD16—44no—
116C2×C8×C11—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131#4325—44no—
132#4323—44no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—82no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141Dic11⋊C4—82no—
142#4318—41no—
143#4318—41no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146#3103D1111yescharacteristic, complemented
147#3036—111no—
148#2580—111no—
149#1517—111no—
150#1487—111no—
151#1478—111no—
152#1286—111no—
153C23×C11—41no—
154C23×C11#12011yescharacteristic
155C22×D11—22no—
156C22×D11—42no—
157C22×D11—42no—
158C22×D11—41no—
159C22×D11—41no—
160Q8×C11—22no—
161Q8×C11—22no—
162Q8×C11—41no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—41no—
166D4×C11—42no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—81no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12711yescharacteristic
189C2×C4×C11C2×SD1611yescharacteristic
190C2×C4×C11#13511yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11#13711yescharacteristic
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198D44—22no—
199D44—22no—
200D44—41no—
201D44—41no—
202C4×D11—82no—
203C4×D11—82no—
204C8×C11—42no—
205C11⋊C8—42no—
206C11⋊C8—81no—
207C2×AGL(1,ℤ/8)—221no—
208#532C2×D1111yescharacteristic
209C2×C4×Q8C2×D1111yescharacteristic
210C2×C4×D4—111no—
211#481—21no—
212#475—21no—
213#463—222no—
214#461—221no—
215#460—21no—
216#459—221no—
217#448—21no—
218C4×SD16—22no—
219#431—111no—
220#431C2×D1111yescharacteristic
221#423—111no—
222#417—221no—
223#399—221no—
224#393—221no—
225#390—221no—
226#389—221no—
227#385—222no—
228#382—111no—
229#327—222no—
230Q8⋊C8—222no—
231D4⋊C8—222no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11#39211yescharacteristic
238C22×C11#44811yescharacteristic
239C22×C11#44911yescharacteristic
240C2×D11—44no—
241C2×D11—42no—
242C2×D11—82no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—42no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11#45011yescharacteristic
253C4×C11#45211yescharacteristic
254C4×C11#46511yescharacteristic
255C4×C11#46811yescharacteristic
256Dic11—82no—
257Dic11—81no—
258C2×#41—21no—
259C22×Q8C22⋊D1111yescharacteristic
260C22×D4—111no—
261C23×C4—221no—
262AGL(1,ℤ/8)—442no—
263AGL(1,ℤ/8)—442no—
264C2×SD16—22no—
265C2×SD16—222no—
266C2×D8—222no—
267C2×M16—221no—
268C4⋊Q8C22⋊D1111yescharacteristic
269#127C22⋊D1111yescharacteristic
270#124—21no—
271#121—21no—
272#121—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—221no—
280C4×D4—221no—
281C4×D4—221no—
282C4×D4—221no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4C22⋊D1111yescharacteristic
288C2×C22⋊C4—222no—
289C2×C22⋊C4—221no—
290C2×C22⋊C4—222no—
291C2×C42—21no—
292C2×C42C22×D1111yescharacteristic
293#106—22no—
294C4⋊C8—21no—
295C4⋊C8—112no—
296C4⋊C8—221no—
297C4⋊C8—221no—
298#103—22no—
299#103—222no—
300#102—22no—
301#102—222no—
302C22⋊C8—21no—
303C22⋊C8—221no—
304C4×C8—221no—
305C4×C8C22⋊D1112yes—
306#95—112no—
307#95—222no—
308#95—221no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11—161no—
312C2×C11#200011yescharacteristic
313C2×C11#200811yescharacteristic
314C2×C11#201011yescharacteristic
315D11—82no—
316C24—221no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41—41no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—42no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4—112no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—221no—
333C2×D4—221no—
334C2×D4—221no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—41no—
338C22×C4—222no—
339C22×C4—221no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—882no—
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346SD16—44no—
347SD16—444no—
348D8—444no—
349M16—441no—
350M16—441no—
351C2×C8—22no—
352C2×C8—222no—
353C2×C8—441no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—221no—
361C4⋊C4—221no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—882no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—444no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C22⋊C4—882no—
371C42—41no—
372C42—41no—
373C42D4×D1111yescharacteristic
374C42#434111yescharacteristic
375C42C2×C22⋊D1111yescharacteristic
376C42C2×C22⋊D1111yescharacteristic
377C11#999811yescharacteristic, complemented, Sylow
378C23—41no—
379C23—222no—
380C23—442no—
381C23—442no—
382C23—441no—
383C23—441no—
384C23#6699011yescharacteristic
385Q8—22no—
386Q8—22no—
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—41no—
391D4—42no—
392D4—41no—
393D4—41no—
394D4—81no—
395D4—81no—
396D4—81no—
397D4—222no—
398D4—222no—
399D4—441no—
400D4—441no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—882no—
418C2×C4—882no—
419C2×C4SD16×D1111yescharacteristic
420C2×C4#6696711yescharacteristic
421C2×C4#6696811yescharacteristic
422C2×C4#6696911yescharacteristic
423C2×C4#6699011yescharacteristic
424C2×C4#6699111yescharacteristic
425C2×C4#6699211yescharacteristic
426C2×C4#6699211yescharacteristic
427C2×C4#6699311yescharacteristic
428C2×C4#6700611yescharacteristic
429C8—42no—
430C8—442no—
431C8—881no—
432C22—21no—
433C22—21no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—444no—
438C22—442no—
439C22—882no—
440C22—881no—
441C22—881no—
442C22#1062278311yescharacteristic
443C22#1062278511yescharacteristic
444C22#1062283611yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—81no—
451C4—81no—
452C4—882no—
453C4—881no—
454C4#1062278211yescharacteristic
455C4#1062278411yescharacteristic
456C4#1062278611yescharacteristic
457C4#1062278711yescharacteristic
458C2—21no—
459C2—21no—
460C2—161no—
461C2—882no—
462C2#1306961611yescharacteristic
463C2#1306966611yescharacteristic
464C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3103C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3103D11
hypocenterC11#9998
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13073974C2semidirect
3. #13067176C2semidirect
4. #13067045C2semidirect
5. #13067008C2semidirect
6. #13066475C2semidirect
7. C11×#3103C2semidirect
111. C2×D44SD16semidirect
146. #3103D11semidirect
377. C11#9998semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130780762
#130739742
#130671762
#130670452
#130670082
#130664752
C11×#31032
#999811